The set of all vectors $\displaystyle V = [v_1 , v_2 , v_3 , v_4]$ ∈ $\displaystyle R^4$ with $\displaystyle v_1+v_2=0$ and $\displaystyle v_3-v_4=1$ is not a vector space.
How can I begin this? I know all 9 properties of vector space, but how to show the proof.

Sep 14th 2009, 05:19 AM

Taluivren

How about the axiom that a vector space has an identity element of addition, zero vector?